If a his-tagged protein must be eluted from Ni-NTA resin by using buffer with imidazole, how imidazole can just simply be removed from the resin using equilibrium buffer only? Can someone clarify it?
If I understand your question correctly - His-tagged proteins are eluted from Ni-NTA resin by Imidazole owing to the Imidazole ring mimicking the side-chain of Histidine residues, thereby displacing the protein. After the protein has been eluted, dialyse the protein against buffer lacking imidazole to remove this.
As far as the resin is concerned, washing the resin with an excess of chromatography buffer after the elution (something simple such as PBS, Hepes-buffered saline etc) is a valid step to remove the vestigial imidazole, prior to washing with a similar volume of mQ water and then storage of the resin with 20% Ethanol. (eventually you will need to regenerate your resin- there are many good protocols for this using EDTA etc).
If Imidazole is a problem, another alternative is to wash the protein following the binding step by using the equilibrating buffer, (for instance, at pH8.0), then washing with the same buffer but with pH modified downwards - i.e. pH7.4 (gentle wash), pH7.0 (less gentle wash), pH6.5 (stringent wash), pH5.5-6.0 (elution) - but again, only do this if your protein tolerates reduced pH.
Affinity of imidazole for NiNTA is much less than the one of hexahistidine for NiNTA. Kd is in the µM range for hexahistidine whereas you need tens-hundreds mM range of imidazole for elution of His tagged proteins(Kd for imidazole must be in the mM range). The fact that hexahistidine is able to interact with three immobilized nickel ions whereas imidazole is interacting only with one Ni explains the difference in observed affinities. Therefore imidazole interaction with NiNTA is not very stable. A simple wash is enough to dilute imidazole,to promote complex dissociation and then wash it away from the NiNTA matrix.